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On a nonorientable
analogue of the Milnor conjecture
Stanislav Jabuka and Cornelia A Van Cott |
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Algebraic & Geometric Topology 21 (2021) 2571–2625
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Abstract |
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The nonorientable –genus of a knot is the smallest first Betti number of any nonorientable surface properly embedded in the –ball and bounding the knot . We study a conjecture proposed by Batson about the value of for torus knots, which can be seen as a nonorientable analogue of Milnor’s conjecture for the orientable –genus of torus knots. We prove the conjecture for many infinite families of torus knots, by calculating for all torus knots a lower bound for formulated by Ozsváth, Stipsicz and Szabó. |
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Keywords
nonorientable 4–genus, 4–dimensional crosscap number, torus
knots
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Mathematical Subject Classification
Primary: 57K10
Secondary: 57R58
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References |
Publication
Received: 22 April 2020
Revised: 31 August 2020
Accepted: 8 December 2020
Published: 31 October 2021
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Authors |
| Stanislav Jabuka | |
| Department of Mathematics and
Statistics University of Nevada, Reno Reno, NV United States |
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| Cornelia A Van Cott | |
| Department of Mathematics University of San Francisco San Francisco, CA United States |
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